# Thread: derivative and tangent line issues

1. ## derivative and tangent line issues

Below, there is a problem that I just cannot solve, I've tried all kinds of ways but nothing works. So by getting a large variety of opinions and solutions, I can be able to solve this problem.

Let f(x) =1/(x-8). Calculate the difference quotient
{f(6+h)-f(6)}/h for
h=.1__
h=.01__
h=-.01__
h=-.1__
If someone now told you that the derivative (slope of the tangent line to the graph) of f(x) at x=6 was -1/n^2 for some integer n what would you expect n to be?
n=__

Thanks you in advance

2. Originally Posted by Skakuntala
Below, there is a problem that I just cannot solve, I've tried all kinds of ways but nothing works. So by getting a large variety of opinions and solutions, I can be able to solve this problem.

Let f(x) =1/(x-8). Calculate the difference quotient
{f(6+h)-f(6)}/h for
h=.1__
h=.01__
h=-.01__
h=-.1__
If someone now told you that the derivative (slope of the tangent line to the graph) of f(x) at x=6 was -1/n^2 for some integer n what would you expect n to be?
n=__

Thanks you in advance
This is not good. It is a simple algebra problem. You haven't forgotten your algebra, have you?

f(x) = 1/(x-8)
f(6) = 1/(6-8) = 1/(-2) = -1/2
f(6+h) = 1/(6+h-8) = 1/(h-2)

Now what?